Asymptotic Expansions for Two Dimensional Symmetrical Laminar Wakes

Abstract

A non parallel extension of the Gaussian asymptotic representation of the two dimensional laminar incompressible far wake past a symmetrical body is presented. Under the one and only condition that the middle and far field be governed by the thin shear layer theory that keeps the complete non linearity of the equation of motion, we determined a solution in terms of an infinite power series of the streamwise space variable with fractional negative exponents. The general n-th order term has been analytically established. The behaviour of these expansions inserted into the Navier-Stokes equations was analyzed to verify the consistency of the approximation in the intermediate region of the wake. At the third order the correction due to pressure variations identically vanishes while the contribution of the longitudinal diffusion is still two-three order of magnitude smaller than that of the transversal diffusion, depending on the Reynolds number.